This topic hits a bit close to home as I've researched extensively on how to get the best video quality out of the TV shows/offline movie collection I have.
If you only care about playing all kinds of media and want ease of installation: A shield TV will do just fine. In fact, the 2020 version also has an AI upscaler which is pretty decent for upconversion of 1080p to 4K. Get the pro version if you also want to use it as a plex server. However, I'd recommend making your PC's hard drives as the plex server and Nvidia as the client. This way, you can set up RAID or other fancy storage on your PC, make your REMUX/BR-rips and directly put it up on plex, you should be able to stream it directly on your shield or any other Android TV box you have.
If you care about the absolute best media playback: Set up an ITX HTPC and put in a GTX 1080 ti or an RTX 2070 super in it. RTX 2060 will also work, but it won't be able to reach max settings. The absolute minimum would be a GTX 1060/1650 super, as below it there's no need to go through all this trouble
Now, download the latest MPC-HC from
their github master and install it. This should contain the latest LAV filters. Now, download and
set up MadVR. Remember, it's a complex procedure and I'd recommend doing it on a weekend. You can overclock the card and try a bit higher settings as well. The above guide helps to set up proper MadVR settings including what upscaling you want, how to do your HDR tone mapping (MadVR's dynamic tone mapping is absolutely crazy good and can even make an HDR10 source look as good as HDR10+/Dolby Vision since all 10+/DV adds is dynamic metadata). Not to mention how great their upscaling and dithering is. You can play absolutely any file and play around with more settings than you want.
Now, let's look at some simple upscaling and rendering results, shall we. I just picked an anime and a TV show (Isekai Quartet and Westworld randomly) to show how it does with both kinds of sources. Both are 1080p 10-bit x265 sources. On 4K the upscaling difference won't be as visible as there'll just be anti-aliasing, though even on 4k sources MadVR looks significantly better than usual media players.
The screenshots exceed the max file size limit, so here they are
on imgur. As you can see, not only is MadVR significantly better with detail and upscaling, even the colour processing looks better (at least on my screen). The differences increase further with HDR content, but they won't be conveyed in taking photos or screenshots.